Monday, April 30, 2012

Mathematics, Intuition, Real World Mathematics Applications. Random Notes.

Edison on the role of theory in his inventions

“I can always hire mathematicians but they can’t hire me.” - Thomas Edison.

Economics and mathematics

John Maynard Keynes, a student of Alfred Marshall, makes a statement in
his General Theory of Employment, Interest and Money (GT) which reflects
Marshall’s statical method: "To large a proportion of recent ‘mathematical’
economics are mere concoctions, as imprecise as the initial assumptions they
rest on,
which allow the author to lose sight of the complexities and
interdependencies of the real world in a maze of pretensions and unhelpful

About proof

The premise may be true because it gives true consequences. Let's prove it later.

Daydreaming is a comfortable investigation of a number of premises that can give true consequences without a need for premises' proofs.

If the consequence is true, for a certain premise, it is a nice sign to go ahead and prove the premise within its axiomatic system.

Even if pure math is clear if contradictions, it can not guarantee that non-axiomatized field of applied math will have meaningful results.

Proof, in any field, with possible exception of mathematics, is often consider convincing, even correct, if the consequences, effects under investigation seem to be reasonably predictable in the whole mash up of a number of non-axiomatized systems and their relationships, in the web of their cause, effect connections. But, that should not put mathematics in any special position, because the proofs in other fields, and the investigation methods, in the way they are, are the best what can be done at the time. If the cause is not axiomatized, the effect can be predicted in only of handful of special cases, which is what we have to deal most of the time anyway.

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